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Problem 2. Brunswick Dairy produces four products: Processed Milk, Fresh Milk, Long-Life Milk, and Yogurt. The raw materials for producing these products, their cost, and available amounts for daily production are shown in the table below.

Raw Material	Amount Available	Cost per Unit
Low Grade raw milk	12,000 Gallons	$0.80 / Gallon
Medium Grade raw milk	11,000 Gallons	$0.90 / Gallon
High Grade raw milk	10,000 Gallons	$1.00 / Gallon
Yogurt Bacteria	25,000 Units	$0.003 / Unit

The production process is accomplished in two separate phases that involve several processes. In the first phase, 1.2 Gallon of Low Grade raw milk, 1 Gallon of Medium Grade raw milk, and 0.8 Gallon of High Grade raw milk are mixed and heated to produce 3 gallons of Processed Milk. The heating cost for those 3 Gallons is $0.10. This Processed Milk is either sold at $3.2/Gallon or processed further.

In the second phase, the Processed Milk can be converted into the final products as follows:

• Fresh Milk is produced by heating Processed Milk to 152 degrees Celsius. It cost $0.30 to convert one gallon of Processed Milk into one gallon of Fresh Milk.
• Long-Life milk is produced by heating Processed Milk to 180 degrees Celsius. It costs $0.35 to convert one gallon of Processed Milk into one gallon of Long-Life Milk.
• Yogurt is produced by a fermenting process where each gallon of Processed Milk is mixed with 14 units of Bacteria. The operation costs $0.40 per gallon and produces 28 units of Yogurt.

The prices for these products are as follows:

Fresh Milk $3.75 /gallon Long sdfgLife Milk $4.25 /gallon

Yogurt $0.40 /unit.

The company wants to maximize its profit from the daily production given that it can sell any quantities of its products. In addition, the company has recently signed a contract with a major supermarket chain to supply it daily with 5000 gallons of Fresh Milk and 1000 gallons of Long-Life Milk. The company also signed another contract with a small cheese factory to supply it daily with 1000 gallons of Processed Milk.

Formulate a linear program to solve this problem. Finally solve this problem using Matlab.

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